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#### Series in "The Belt and Road" International Railway Talents Education: Fundamentals of Structural Dynamics

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Chapter 1 Overview of Structural Dynamics
1.1 Objective of structural dynamic analysis
1.2 Characteristics of structural dynamics
1.3 Classification of vibrations
1.4 Vibration problems in engineering
1.5 Procedures of dynamic response analysis of structures
Problems
References
Chapter 2 Formulation of Equations of Motion of Systems
2.1 System constraints
2.2 Representation of system configuration
2.3 Real displacements, possible displacements and virtual displacements
2.4 Generalized force
2.5 Conservative force and potential energy
2.6 Direct equilibrium method
2.7 Principle of virtual displacements
2.8 Lagrange's equation
2.9 Hamilton's principle
2.10 Principle of total potential energy with a stationary value in elastic syste m dynamics
2.11 The 'set-in-right-position'rule for assembling system matrices and method of
computer implementation in Matlab
Problems
References
Chapter 3 Analysis of Dynamic Response of SDOF Systems
3.1 Analysis of free vibrations
3.2 Response of SDOF systems to harmonic loads
3.3 Vibration caused by base motion and vibration isolation
3.4 Introduction to damping theory
3.5 Evaluation of viscous-damping ratio
3.6 Response of SDOF systems to periodic loads
3.7 Response of SDOF systems to impulsive loads
3.8 Time domain analysis of dynamic response to arbitrary dynamic loads
3.9 Frequency domain analysis of dynamic response to arbitrary dynamic loads
Problems
References
Chapter 4 Analysis of Dynamic Response of MDOF Systems: Mode Superposition Method
4.1 Analysis of dynamic properties of MDOF systems
4.2 Coupling characteristics and uncoupling procedure of equations of MDOF systems
4.3 Analysis of free vibration response of undamped systems
4.4 Response of undamped systems to arbitrary dynamic loads
4.5 Response of damped systems to arbitrary dynamic loads
Problems
References
Chapter 5 Analysis of Dynamic Response of Continuous Systems:Straight beam
5.1 Differential equations of motion of undamped straight beam
5.2 Modal expansion of displacement and orthogonality of mode shapes of straight beam
5.3 Free vibration analysis of undamped straight beam
5.4 Forced vibration analysis of undamped straight beam
5.5 Forced vibration analysis of damped straight beam
Problems
References
Chapter 6 Approximate Evaluation of Natural Frequencies and Mode Shapes
6.1 Rayleigh energy method
6.2 Rayleigh-Ritz method
6.3 Matrix iteration method
6.4 Subspace iteration method
6.5 Reduction of degrees of freedom in dynamic analysis
Problems
References
Chapter 7 Step-by-step Integration Method
7.1 Basic idea of step-by-step integration method
7.2 Linear acceleration method
7.3 Wilson-0 method
7.4 Newmark method
7.5 Stability and accuracy of step-by-step integration method
Problems
References
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